FOR TEACHERS ONLY
The University of the State of New York
REGENTS HIGH SCHOOL EXAMINATION
INTEGRATED ALGEBRA
Thursday, June 18, 2015 — 9:15 a.m. to 12:15 p.m., only
SCORING KEY AND RATING GUIDE
Mechanics of Rating
The following procedures are to be followed for scoring student answer papers for the Regents Examination in Integrated Algebra. More detailed information about scoring is provided in the publication Information Booklet for Scoring the Regents Examinations in
Mathematics.Do not attempt to correct the student’s work by making insertions or changes of any kind. In scoring the open-ended questions, use check marks to indicate student errors.
Unless otherwise specified, mathematically correct variations in the answers will be allowed.
Units need not be given when the wording of the questions allows such omissions.
Each student’s answer paper is to be scored by a minimum of three mathematics teachers. No one teacher is to score more than approximately one-third of the open-ended questions on a student’s paper. Teachers may not score their own students’ answer papers.
On the student’s separate answer sheet, for each question, record the number of credits earned and the teacher’s assigned rater/scorer letter.
Schools are not permitted to rescore any of the open-ended questions on this exam after each question has been rated once, regardless of the final exam score.
Schools are required to ensure that the raw scores have been added correctly and that the resulting scale score has been determined accurately.
Raters should record the student’s scores for all questions and the total raw score on the
student’s separate answer sheet. Then the student’s total raw score should be converted to a
scale score by using the conversion chart that will be posted on the Department’s web site
at: http://www.p12.nysed.gov/assessment/ on Thursday, June 18, 2015. Because scale scores
corresponding to raw scores in the conversion chart may change from one administration to
another, it is crucial that, for each administration, the conversion chart provided for that
administration be used to determine the student’s final score. The student’s scale score
should be entered in the box provided on the student’s separate answer sheet. The scale score
is the student’s final examination score.
If the student’s responses for the multiple-choice questions are being hand scored prior to being scanned, the scorer must be careful not to make any marks on the answer sheet except to record the scores in the designated score boxes. Marks elsewhere on the answer sheet will interfere with the accuracy of the scanning.
Part I
Allow a total of 60 credits, 2 credits for each of the following.
(1) . . . 3 . . . . .
(2) . . . 3 . . . . .
(3) . . . 4 . . . . .
(4) . . . 4 . . . . .
(5) . . . 3 . . . . .
(6) . . . 3 . . . . .
(7) . . . 4 . . . . .
(8) . . . 1 . . . . .
(9) . . . 4 . . . . .
(10) . . . 4 . . . . .
(11) . . . 3 . . . . .
(12) . . . 3 . . . . .
(13) . . . 1 . . . . .
(14) . . . 2 . . . . .
(15) . . . 1 . . . . .
(16) . . . 2 . . . . .
(17) . . . 1 . . . . .
(18) . . . 2 . . . . .
(19) . . . 3 . . . . .
(20) . . . 2 . . . . .
(21) . . . 1 . . . . .
(22) . . . 1 . . . . .
(23) . . . 2 . . . . .
(24) . . . 4 . . . . .
(25) . . . 3 . . . . .
(26) . . . 1 . . . . .
(27) . . . 2 . . . . .
(28) . . . 1 . . . . .
(29) . . . 3 . . . . .
(30) . . . 2 . . . . .
Updated information regarding the rating of this examination may be posted on the New York State Education Department’s web site during the rating period. Check this web site at:
http://www.p12.nysed.gov/assessment/ and select the link “Scoring Information” for any recently posted information regarding this examination. This site should be checked before the rating process for this examination begins and several times throughout the Regents Examination period.
Beginning in January 2013, the Department is providing supplemental scoring guidance, the “Sample Response Set,” for the Regents Examination in Integrated Algebra. This guidance is not required as part of the scorer training. It is at the school’s discretion to incorporate it into the scorer training or to use it as supplemental information during scoring. While not reflective of all scenarios, the sample student responses selected for the Sample Response Set illustrate how less common student responses to open-ended questions may be scored. The Sample Response Set will be available on the Department’s web site at http://www.nysedregents.org/IntegratedAlgebra/.
General Rules for Applying Mathematics Rubrics
I. General Principles for Rating
The rubrics for the constructed-response questions on the Regents Examination in Integrated Algebra are designed to provide a systematic, consistent method for awarding credit. The rubrics are not to be considered all-inclusive; it is impossible to anticipate all the different methods that students might use to solve a given problem. Each response must be rated carefully using the teacher’s professional judgment and knowledge of mathematics; all calculations must be checked. The specific rubrics for each question must be applied consistently to all responses. In cases that are not specifically addressed in the rubrics, raters must follow the general rating guidelines in the publication Information Booklet for Scoring the Regents Examinations in Mathematics, use their own professional judgment, confer with other mathematics teachers, and/or contact the State Education Department for guidance. During each Regents Examination administration period, rating questions may be referred directly to the Education Department. The contact numbers are sent to all schools before each administration period.
II. Full-Credit Responses
A full-credit response provides a complete and correct answer to all parts of the question. Sufficient work is shown to enable the rater to determine how the student arrived at the correct answer.
When the rubric for the full-credit response includes one or more examples of an acceptable method for solving the question (usually introduced by the phrase “such as”), it does not mean that there are no additional acceptable methods of arriving at the correct answer. Unless otherwise specified, mathematically correct alternative solutions should be awarded credit. The only exceptions are those questions that specify the type of solution that must be used; e.g., an algebraic solution or a graphic solution. A correct solution using a method other than the one specified is awarded half the credit of a correct solution using the specified method.
III. Appropriate Work
Full-Credit Responses: The directions in the examination booklet for all the constructed-response questions state: “Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc.” The student has the responsibility of providing the correct answer and showing how that answer was obtained. The student must “construct” the response; the teacher should not have to search through a group of seemingly random calculations scribbled on the student paper to ascertain what method the student may have used.
Responses With Errors: Rubrics that state “Appropriate work is shown, but…” are intended to be used with solutions that show an essentially complete response to the question but contain certain types of errors, whether computational, rounding, graphing, or conceptual. If the response is incomplete; i.e., an equation is written but not solved or an equation is solved but not all of the parts of the question are answered, appropriate work has not been shown. Other rubrics address incomplete responses.
IV. Multiple Errors
Computational Errors, Graphing Errors, and Rounding Errors: Each of these types of errors results in a 1- credit deduction. Any combination of two of these types of errors results in a 2-credit deduction. No more than 2 credits should be deducted for such mechanical errors in any response. The teacher must carefully review the student’s work to determine what errors were made and what type of errors they were.
Conceptual Errors: A conceptual error involves a more serious lack of knowledge or procedure. Examples of conceptual errors include using the incorrect formula for the area of a figure, choosing the incorrect trigonometric function, or multiplying the exponents instead of adding them when multiplying terms with exponents. A response with one conceptual error can receive no more than half credit.
If a response shows repeated occurrences of the same conceptual error, the student should not be penalized twice. If the same conceptual error is repeated in responses to other questions, credit should be deducted in each response.
If a response shows two (or more) different major conceptual errors, it should be considered completely incorrect and receive no credit.
If a response shows one conceptual error and one computational, graphing, or rounding error, the teacher must award credit that takes into account both errors; i.e., awarding half credit for the conceptual error and deducting 1 credit for each mechanical error (maximum of two deductions for mechanical errors).
Part II
For each question, use the specific criteria to award a maximum of 2 credits. Unless other wise specified, mathematically correct alternative solutions should be awarded appropriate credit.
(31) [2] 61.8, and correct work is shown.
[1] An appropriate expression is shown, but one computational or rounding error is made.
or
[1] An appropriate expression is shown, but one conceptual error is made.
or
[1] or an equivalent expression, but no further correct work is shown.
or
[1] 61.8, but no work is shown.
[0] A zero response is completely incorrect, irrelevant, or incoherent or is a correct response that was obtained by an obviously incorrect procedure.
(32) [2] and correct work is shown, such as a labeled diagram.
[1] Appropriate work is shown, but one computational error is made. An appropriate perimeter is found.
or
[1] Appropriate work is shown, but one conceptual error is made. An appropriate perimeter is found.
or
[1] Appropriate work is shown, but the perimeter is expressed as a decimal.
or
[1] , but not work is shown.
[0] A zero response is completely incorrect, irrelevant, or incoherent or is a correct response that was obtained by an obviously incorrect procedure.
7 3 7 3
170 234
(33) [2] x
2⫹ 10x ⫺ 24 ⫽ 0, and correct work is shown.
[1] Appropriate work is shown, but one computational error is made. An appropriate quadratic equation is written.
or
[1] Appropriate work is shown, but one conceptual error is made, such as writing the expression x
2⫹ 10x ⫺ 24.
or
[1] (x ⫹ 12)(x ⫺ 2) ⫽ 0, but no further correct work is shown.
or
[1] x
2⫹ 10x ⫺ 24 ⫽ 0, but no work is shown.
[0] A zero response is completely incorrect, irrelevant, or incoherent or is a correct
response that was obtained by an obviously incorrect procedure.
Part III
For each question, use the specific criteria to award a maximum of 3 credits. Unless otherwise specified, mathematically correct alternative solutions should be awarded appropriate credit.
(34) [3] x ⫽ ⫺1 and (⫺1,2) or equivalent, and correct algebraic work is shown.
[2] Appropriate work is shown, but one computational error is made.
or
[2] Appropriate work is shown to find (⫺1,2), but the axis of symmetry is not stated or is stated incorrectly.
[1] Appropriate work is shown, but two or more computational errors are made.
or
[1] Appropriate work is shown, but one conceptual error is made.
or
[1] Appropriate work is shown to find x ⫽ ⫺1, but no further correct work is shown.
or
[1] x ⫽ ⫺1 and (⫺1,2), but a method other than algebraic is used.
or
[1] x ⫽ ⫺1 and (⫺1,2), but no work is shown.
[0] x ⫽ ⫺1 or (⫺1,2), but no work is shown.
or
[0] A zero response is completely incorrect, irrelevant, or incoherent or is a correct
response that was obtained by an obviously incorrect procedure.
(35) [3] 0.025 and correct work is shown.
[2] Appropriate work is shown, but one computational or rounding error is made.
An appropriate answer is found.
or
[2] is written, but no further correct work is shown.
[1] Appropriate work is shown, but two or more computational errors are made.
An appropriate answer is found.
or
[1] Appropriate work is shown, but one conceptual error is made. An appropriate answer is found.
or
[1] is written, but no further correct work is shown.
or
[1] 0.025, but no work is shown.
[0] Appropriate work is shown to find 1512 and 1551.25, but no further correct work is shown.
or
[0] A zero response is completely incorrect, irrelevant, or incoherent or is a correct response that was obtained by an obviously incorrect procedure.
39 25 1551 25
. .
1551 25 1512 1551 25
. .
⫺
(36) [3] The frequency table is completed correctly, and a correct frequency histogram is drawn and labeled.
[2] The frequency table is completed correctly, but one graphing or labeling error is made.
or
[2] An incorrect frequency table is shown, but an appropriate frequency histogram is drawn and labeled.
[1] The frequency table is completed correctly, but two or more graphing or labeling errors are made.
or
[1] Appropriate work is shown, but one conceptual error is made, such as drawing a bar graph.
or
[1] The frequency table is completed correctly, but no further correct work is shown.
or
[0] A zero response is completely incorrect, irrelevant, or incoherent or is a correct
response that was obtained by an obviously incorrect procedure.
Part IV
For each question, use the specific criteria to award a maximum of 4 credits. Unless otherwise specified, mathematically correct alternative solutions should be awarded appropriate credit.
(37) [4] A correct graph is drawn and ⫺1 and 3 are stated.
[3] One graphing error is made. Appropriate roots are stated.
or
[3] A correct graph is drawn, but only ⫺1 or 3 is stated.
or
[3] A correct graph is drawn, but the roots are expressed as the coordinates (⫺1,0) and (3,0).
[2] Two or more graphing errors are made. Appropriate roots are stated.
or
[2] Appropriate work is shown, but one conceptual error is made. Appropriate roots are stated.
or
[2] Appropriate work is shown to find ⫺1 and 3, but no graph is drawn.
or
[2] A correct graph is drawn, but no further correct work is shown.
[1] Two or more graphing errors are made and roots are stated incorrectly or not stated.
or
[1] Appropriate work is shown, but one conceptual error and one graphing error are made. Appropriate roots are stated.
or
[1] ⫺1 and 3 are stated, but no graph or work is shown.
[0] (–1,0) and (3,0) are stated, but no graph is drawn.
or
[0] A zero response is completely incorrect, irrelevant, or incoherent or is a correct
response that was obtained by an obviously incorrect procedure.
(38) [4] Perimeter 2x
2⫹ 14x ⫹ 4 and area 4x
3⫹ 12x
2⫹ 8x, and correct work is shown.
[3] Appropriate work is shown, but one computational error is made.
or
[2] Appropriate work is shown but two or more computational errors are made.
or
[2] Appropriate work is shown, but one conceptual error is made.
or
[2] Appropriate work is shown to find either perimeter 2x
2⫹ 14x ⫹ 4 or area 4x
3⫹ 12x
2⫹ 8x.
[1] Appropriate work is shown, but one conceptual error and one computational error are made.
or
[1] Perimeter 2x
2⫹ 14x ⫹ 4 and area 4x
3⫹ 12x
2⫹ 8x, but no work is shown.
[0] A zero response is completely incorrect, irrelevant, or incoherent or is a correct
response that was obtained by an obviously incorrect procedure.
(39) [4] 0.25 ⫹ 0.10(m ⫺ 4) ⱕ 2.10 or an equivalent is written, and 22, and correct work is shown.
[3] A correct inequality is written, but one computational error is made. An appropriate number of minutes is stated.
or
[3] A correct inequality is written and solved to find m ⱕ 22.5, but no further correct work is shown.
[2] A correct inequality is written, but two or more computational errors are made.
or
[2] Appropriate work is shown, but one conceptual error is made. An appropriate number of minutes is stated.
or
[2] 0.25 ⫹ 0.10m ⱕ 2.10 is written, and 18, and appropriate work is shown.
or
[2] A correct inequality is written, but no further correct work is shown.
or
[2] 22, but a method other than algebraic is used.
[1] Appropriate work is shown, but one conceptual error and one computational error are made. An appropriate number of minutes is stated.
or
[1] 0.25 ⫹ 0.10m ⱕ 2.10 is written and solved to find m ⱕ 18.5, but no further correct work is shown.
or
[1] 22, but no work is shown.
[0] A zero response is completely incorrect, irrelevant, or incoherent or is a correct
response that was obtained by an obviously incorrect procedure.
Map to Core Curriculum
Regents Examination in Integrated Algebra June 2015
Chart for Converting Total Test Raw Scores to Final Examination Scores (Scale Scores)
Online Submission of Teacher Evaluations of the Test to the Department Suggestions and feedback from teachers provide an important contribution to the test development process. The Department provides an online evaluation form for State assessments. It contains spaces for teachers to respond to several specific questions and to make suggestions. Instructions for completing the evaluation form are as follows:
1. Go to http://www.forms2.nysed.gov/emsc/osa/exameval/reexameval.cfm.
2. Select the test title.
3. Complete the required demographic fields.
4. Complete each evaluation question and provide comments in the space provided.
The Chart for Determining the Final Examination Score for the June 2015 Regents Examination in Integrated Algebra will be posted on the Department’s web site at:
http://www.p12.nysed.gov/assessment/ on Thursday, June 18, 2015. Conversion charts provided for previous administrations of the Regents Examination in Integrated Algebra must NOT be used to determine students’ final scores for this administration.
